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- W2885386320 abstract "We introduce the concept of virtual large cardinals and apply it to obtain a hierarchy of new large cardinal notions between ineffable cardinals and 0#. Given a large cardinal notion A characterized by the existence of elementary embeddings j:Vα→Vβ satisfying some list of properties, we say that a cardinal is virtually A if the embeddings j:VαV→VβV exist in the generic multiverse of V. Unlike their ideological cousins generic large cardinals, virtual large cardinals are actual large cardinals that are compatible with V=L. We study virtual versions of extendible, n-huge, and rank-into-rank cardinals and determine where they fit into the large cardinal hierarchy." @default.
- W2885386320 created "2018-08-22" @default.
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- W2885386320 date "2018-12-01" @default.
- W2885386320 modified "2023-10-01" @default.
- W2885386320 title "Virtual large cardinals" @default.
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- W2885386320 doi "https://doi.org/10.1016/j.apal.2018.08.005" @default.
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